{"id":"https://openalex.org/W2027200819","doi":"https://doi.org/10.1137/07070139x","title":"Strict Efficiency in Set-Valued Optimization","display_name":"Strict Efficiency in Set-Valued Optimization","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2027200819","doi":"https://doi.org/10.1137/07070139x","mag":"2027200819"},"language":"en","primary_location":{"id":"doi:10.1137/07070139x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07070139x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3270978","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073555271","display_name":"Fabi\u00e1n Flores-Baz\u00e1n","orcid":"https://orcid.org/0000-0003-2485-7861"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fabi\u00e1n Flores-Baz\u00e1n","raw_affiliation_strings":["fflores@ing-mat.udec.cl#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"fflores@ing-mat.udec.cl#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069972821","display_name":"Bienvenido Jim\u00e9nez","orcid":"https://orcid.org/0000-0003-1513-8590"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bienvenido Jim\u00e9nez","raw_affiliation_strings":["bjimenez@ind.uned.es#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"bjimenez@ind.uned.es#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1615,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.94279923,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"48","issue":"2","first_page":"881","last_page":"908"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9620000123977661,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8715584874153137},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.8002545833587646},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7771472930908203},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.6314842104911804},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5822792649269104},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.5079665780067444},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5068133473396301},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5039963126182556},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4798561930656433},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45129674673080444},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4472879469394684},{"id":"https://openalex.org/keywords/set-function","display_name":"Set function","score":0.4371567368507385},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.42413175106048584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4214090406894684},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3493525981903076},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.31161630153656006},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17851394414901733},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09045934677124023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8715584874153137},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8002545833587646},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7771472930908203},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.6314842104911804},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5822792649269104},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.5079665780067444},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5068133473396301},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5039963126182556},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4798561930656433},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45129674673080444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4472879469394684},{"id":"https://openalex.org/C15312841","wikidata":"https://www.wikidata.org/wiki/Q1657198","display_name":"Set function","level":3,"score":0.4371567368507385},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.42413175106048584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4214090406894684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3493525981903076},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.31161630153656006},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17851394414901733},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09045934677124023},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/07070139x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07070139x","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:americanae.aecid.es:3270978","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3270978","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:americanae.aecid.es:3332660","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3332660","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/135271","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/135271","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:localhost:10533/142655","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/142655","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:americanae.aecid.es:3270978","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3270978","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W92633816","https://openalex.org/W152727406","https://openalex.org/W336414565","https://openalex.org/W834472104","https://openalex.org/W1501788645","https://openalex.org/W1582299569","https://openalex.org/W1966587106","https://openalex.org/W1967571778","https://openalex.org/W1967619906","https://openalex.org/W1972451512","https://openalex.org/W1975708545","https://openalex.org/W1978409097","https://openalex.org/W1980549717","https://openalex.org/W1984538196","https://openalex.org/W1994120194","https://openalex.org/W2005187615","https://openalex.org/W2013780280","https://openalex.org/W2016066906","https://openalex.org/W2022828798","https://openalex.org/W2024057042","https://openalex.org/W2035990529","https://openalex.org/W2045552614","https://openalex.org/W2057088466","https://openalex.org/W2057357578","https://openalex.org/W2057404142","https://openalex.org/W2062813253","https://openalex.org/W2066360128","https://openalex.org/W2071192910","https://openalex.org/W2075308281","https://openalex.org/W2077581281","https://openalex.org/W2081616665","https://openalex.org/W2085163586","https://openalex.org/W2094964517","https://openalex.org/W4242190958"],"related_works":["https://openalex.org/W3194235253","https://openalex.org/W2766340440","https://openalex.org/W2565276936","https://openalex.org/W4385713703","https://openalex.org/W2039939787","https://openalex.org/W2126999288","https://openalex.org/W109016340","https://openalex.org/W179906810","https://openalex.org/W188711498","https://openalex.org/W2363819650"],"abstract_inverted_index":{"In":[0,27],"this":[1],"paper,":[2],"we":[3,33,100],"develop":[4],"the":[5,77,82,86,124],"notion":[6],"of":[7,41,53,57,65,76,85,96,113,126],"a":[8,14,36,39,42,51,54,63,69,74],"$\\phi$-minimizer":[9,40,52],"(or":[10],"strict":[11,66],"efficiency)":[12],"for":[13],"set-valued":[15],"map.":[16],"Its":[17],"properties":[18],"and":[19,46,99],"relations":[20],"with":[21],"other":[22],"similar":[23],"notions":[24],"are":[25,129],"studied.":[26],"special":[28],"circumstances,":[29],"under":[30],"suitable":[31],"conditions,":[32],"prove":[34],"that":[35],"point":[37],"is":[38,50,73,92],"vector":[43],"function":[44,79],"if":[45,48],"only":[47],"it":[49],"certain":[55],"family":[56],"linear":[58],"scalarizations.":[59],"We":[60],"also":[61,130],"establish":[62],"characterization":[64],"efficiency":[67],"through":[68,110],"nonlinear":[70],"scalarization,":[71],"which":[72],"generalization":[75],"Gerstewitz":[78],"defined":[80],"on":[81,94],"power":[83],"set":[84],"image":[87],"space.":[88],"The":[89],"final":[90],"part":[91],"focused":[93],"minimizers":[95],"order":[97],"one,":[98],"provide":[101],"several":[102],"necessary":[103],"or":[104],"sufficient":[105],"conditions":[106],"(without":[107],"convexity":[108],"assumptions)":[109],"different":[111],"kinds":[112],"derivatives":[114],"as":[115],"contingent,":[116],"radial":[117],"among":[118],"others.":[119],"Various":[120],"illustrative":[121],"examples":[122],"showing":[123],"applicability":[125],"our":[127],"results":[128],"presented.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-26T07:53:14.480251","created_date":"2025-10-10T00:00:00"}
